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Dependence properties of dynamic credit risk models

Author

Listed:
  • Bäuerle Nicole
  • Schmock Uwe

    (Institute for Mathematical Methods in Economics, Vienna University of Technology, Vienne, Österreich)

Abstract

We give a unified mathematical framework for reduced-form models for portfolio credit risk and identify properties which lead to positive dependence of default times. Dependence in the default hazard rates is modeled by common macroeconomic factors as well as by inter-obligor links. It is shown that popular models produce positive dependence between defaults in terms of association. Implications of these results are discussed, in particular when we turn to pricing of credit derivatives. In mathematical terms our paper contains results about association of a class of non-Markovian processes.

Suggested Citation

  • Bäuerle Nicole & Schmock Uwe, 2012. "Dependence properties of dynamic credit risk models," Statistics & Risk Modeling, De Gruyter, vol. 29(3), pages 243-268, August.
  • Handle: RePEc:bpj:strimo:v:29:y:2012:i:3:p:243-268:n:3
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    References listed on IDEAS

    as
    1. Nicole Bäuerle & Anja Blatter & Alfred Müller, 2008. "Dependence properties and comparison results for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 161-186, February.
    2. Ebrahimi, Nader, 2002. "On the Dependence Structure of Certain Multi-dimensional Ito Processes and Corresponding Hitting Times," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 128-137, April.
    3. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    4. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    5. Fan Yu, 2007. "Correlated Defaults In Intensity-Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173.
    6. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515 World Scientific Publishing Co. Pte. Ltd..
    7. repec:spr:compst:v:67:y:2008:i:1:p:161-186 is not listed on IDEAS
    8. Damiano Brigo & Agostino Capponi, 2008. "Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps," Papers 0812.3705, arXiv.org, revised Nov 2009.
    9. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
    10. Masaaki Kijima, 1998. "Monotonicities in a Markov Chain Model for Valuing Corporate Bonds Subject to Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 229-247.
    11. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    12. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
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